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C72×Dic31⋊C5 #44477129

order30380
automorphism?
homologyAbelianization (H1) = C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×Dic31⋊C5
unambiguous semidirect productDic31⋊(C5×C72)
unambiguous semidirect productΓL(1,𝔽32)⋊(C4×C72)
unambiguous semidirect product(C7×Dic31)⋊(C5×C7)
unambiguous semidirect product(C72×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C5×C72
HallC72×ΓL(1,𝔽32) ⋊ C4
HallC72×Dic31 ⋊ C5
HallC72×C31 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C4×C72
HallDic31 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72D31⋊C5
commutator, hypocenterC31C4×C5×C72
FrattiniC2C72×D31⋊C5
Fitting, socleC2×C72×C31C2×C5
prime radicalC2×C72×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C72
LCSG ▷ C31
UCSC1 ◁ C2×C72

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6076

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 38);