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C22⋊C4×D1181 #49180353

order37792
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D1181

Splittings

FittingC22⋊C4×C1181 ⋊ C2
SylowC1181 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1181
commutatorC2×C1181C22×C4
FittingC22⋊C4×C1181C2
socle, cosocleC22×C1181C23
prime radicalC23×D1181C2
hypercenterC22⋊C4D1181
hypocenterC1181C2×C22⋊C4
LCSG ▷ C2×C1181 ▷ C1181
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9448

Conjugacy classes & character table

5920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37792, 96);