Finite Group Databasebeta

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C4⋊C4×D761 #37566853

order24352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D761

Splittings

FittingC4⋊C4×C761 ⋊ C2
SylowC761 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D761
commutatorC2×C761C22×C4
FittingC4⋊C4×C761C2
socle, cosocleC22×C761C23
prime radicalC22×D761C22
hypercenterC4⋊C4D761
hypocenterC761C2×C4⋊C4
LCSG ▷ C2×C761 ▷ C761
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12176

Conjugacy classes & character table

3820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 99);