Finite Group Databasebeta

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C5×C13×Dic105 #41031445

order27300
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic105
unambiguous semidirect productC3⋊(C5×C13×Dic35)
unambiguous semidirect productC7⋊(C5×C13×Dic15)

Splittings

derivedC3×C5×C7 ⋊ C4×C5×C13
HallC3×C52×C7×C13 ⋊ C4
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ Dic7
HallC3×C52×C7 ⋊ C4×C13
HallC52×C13 ⋊ Dic21
HallC3×C7×C13 ⋊ C5×Dic5
HallC52×C7 ⋊ Dic3×C13
HallC7×C13 ⋊ C5×Dic15
HallC3×C52 ⋊ C13×Dic7
HallC3×C13 ⋊ C5×Dic35
SylowC52 ⋊ C13×Dic21
HallC3×C7 ⋊ C5×C13×Dic5
SylowC7 ⋊ C5×C13×Dic15
SylowC3 ⋊ C5×C13×Dic35

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D105
commutator, hypocenterC3×C5×C7C4×C5×C13
FrattiniC2C5×C13×D105
Fitting, socle, prime radicalC2×C3×C52×C7×C13C2
cosocleC2×C3×C5×C7C2×C5×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C5×C13

128 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

7020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 335);