Finite Group Databasebeta

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C4⋊C4×C47⋊C16 #26131622

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

Aliases

direct productC4⋊C4×C47⋊C16

Splittings

SylowC47 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D47
commutatorC2×C47C2×C4×C16
FittingC8×C4⋊C4×C47C2
socle, prime radicalC23×C47C22×C8
cosocleC22×C8×C47C23
hypercenterC8×C4⋊C4D47
hypocenterC47C16×C4⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84912);