Finite Group Databasebeta

C2×#20259845 #27135686

order12352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20259845

Splittings

SylowC193 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#15690540
commutator, cosocleC8×C193C23
FrattiniC8C22×D193
FittingC2×Q16×C193C2
socle, prime radicalC22×C193D8
hypercenterC2×Q16D193
hypocenterC193C2×Q32
LCSG ▷ C8×C193 ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 976);