Finite Group Databasebeta

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C4⋊C4×D743 #37557932

order23776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D743

Splittings

FittingC4⋊C4×C743 ⋊ C2
SylowC743 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D743
commutatorC2×C743C22×C4
FittingC4⋊C4×C743C2
socle, cosocleC22×C743C23
prime radicalC22×D743C22
hypercenterC4⋊C4D743
hypocenterC743C2×C4⋊C4
LCSG ▷ C2×C743 ▷ C743
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11888

Conjugacy classes & character table

3730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23776, 99);