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C4⋊C4×D1181 #49180356

order37792
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D1181

Splittings

FittingC4⋊C4×C1181 ⋊ C2
SylowC1181 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1181
commutatorC2×C1181C22×C4
FittingC4⋊C4×C1181C2
socle, cosocleC22×C1181C23
prime radicalC22×D1181C22
hypercenterC4⋊C4D1181
hypocenterC1181C2×C4⋊C4
LCSG ▷ C2×C1181 ▷ C1181
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18896

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, 99);