Finite Group Databasebeta

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C4×C4⋊(C47⋊C16) #26131583

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊(C47⋊C16)

Splittings

SylowC47 ⋊ C4×C4⋊C16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC22×C8C22×D47
FittingC42×C8×C47C2
socle, prime radicalC23×C47C22×C8
cosocleC22×C8×C47C23
hypercenterC42×C8D47
hypocenterC47C4×C4⋊C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84873);