Finite Group Databasebeta

C4×Q8×C47⋊C8 #26214886

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×Q8×C47⋊C8

Splittings

SylowC47 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC42×Q8×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC42×Q8D47
hypocenterC47C4×C8×Q8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C42×Q8

1070 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, 168176);