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C72×C13×Dic15 #50303685

order38220
automorphism?
homologyAbelianization (H1) = C4×C72×C13 · Schur multiplier (H2) = C7

Aliases

direct productC72×C13×Dic15
unambiguous semidirect productC3⋊(C72×C13×Dic5)

Splittings

derived, HallC3×C5 ⋊ C4×C72×C13
HallC3×C5×C72×C13 ⋊ C4
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ C4×C13
HallC5×C72 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C4×C72
HallC3×C72 ⋊ C13×Dic5
HallC5×C13 ⋊ C72×Dic3
HallC3×C13 ⋊ C72×Dic5
SylowC5 ⋊ C72×Dic3×C13
SylowC3 ⋊ C72×C13×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C72×C13D15
commutator, hypocenterC3×C5C4×C72×C13
FrattiniC2C72×C13×D15
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C3×C5C2×C72×C13
LCSG ▷ C3×C5
UCSC1 ◁ C2×C72×C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38220

Conjugacy classes & character table

11466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 371);