Finite Group Databasebeta

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C7×C13×C3⋊#1042 #41032001

order27300
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×C3⋊#1042
unambiguous semidirect productC3⋊(C7×C13×#1042)

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C4
derived, HallC3×C52 ⋊ C4×C7×C13
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C13
HallC52×C13 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ #1042
HallC52×C7 ⋊ Dic3×C13
HallC3×C13 ⋊ C7×#1042
SylowC52 ⋊ C7×Dic3×C13
HallC3×C7 ⋊ C13×#1042
SylowC3 ⋊ C7×C13×#1042

Subgroups

subgroupG/H
center, hypercenterC7×C13C3⋊#1042
commutator, hypocenterC3×C52C4×C7×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C5×C7×D5×C13C2
cosocleC3×C5×D5C2×C7×C13
LCSG ▷ C3×C52
UCSC1 ◁ C7×C13

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

normal subgroups only

This group has 104 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) = 5460

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 891);