Finite Group Databasebeta

C2×#20259817 #27135238

order12352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20259817

Splittings

SylowC193 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#15690532
commutatorC22×C193C22×C4
FrattiniC2×C4C22×D193
FittingC2×M16×C193C2
socleC22×C193C22⋊C4
prime radicalC23×C193C2×C4
cosocleC2×C4×C193C23
hypercenterC2×M16D193
hypocenterC193C2×#101
LCSG ▷ C22×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1942 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 528);