Finite Group Databasebeta

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C5×#19129703 #41031374

order27300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#19129703

Splittings

derivedC5×C7×C13 ⋊ C3×C4×C5
HallC5×Dic455 ⋊ C3
HallC52×C7×C13⋊C3 ⋊ C4
HallC52×C7×C13 ⋊ C3×C4
HallC52×C13⋊C3 ⋊ Dic7
HallC52×C13 ⋊ C3×Dic7
HallC7×C13⋊C3 ⋊ C5×Dic5
HallC52×C7 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×C5×Dic5
HallC13⋊C3 ⋊ C5×Dic35
SylowC52 ⋊ #11763955
SylowC13 ⋊ C3×C5×Dic35
SylowC7 ⋊ C5×Dic65⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊((C13⋊C3)⋊D7)
commutator, hypocenterC5×C7×C13C3×C4×C5
FrattiniC2C5×C5⋊((C13⋊C3)⋊D7)
Fitting, socleC2×C52×C7×C13C2×C3
prime radicalC2×C52×C7×C13⋊C3C2
cosocleC2×C5×C7×C13C2×C3×C5
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 1820

Conjugacy classes & character table

1270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 264);