Finite Group Databasebeta

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C4×#15689034 #26138080

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC4×#15689034

Splittings

FittingC22×C4×Q8×C47 ⋊ C2
SylowC47 ⋊ C4×#393

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×C4×Q8×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC22×C4×Q8D47
hypocenterC47C4×#393
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

2158 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 91370);