Finite Group Databasebeta

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C2×#20243363 #26215619

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243363

Splittings

SylowC47 ⋊ C2×#1796

Subgroups

subgroupG/H
centerC22#15688979
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC22×2−1+4×C47C2
socleC22×C47#379
cosocleC22×C4×C47C24
hypercenterC22×2−1+4D47
hypocenterC47C2×#1796
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×2−1+4

3602 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1622 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168909);