Finite Group Databasebeta

C2×#20259987 #27136336

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20259987

Splittings

SylowC193 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#11715871
commutatorC2×C193C23×C4
FrattiniC2C23×#11715871
FittingC2×Q8×C193C4
socleC22×C193C22×C4
prime radicalC2×#15690556C2
cosocleDic193C24
hypercenterC2×Q8#11715871
hypocenterC193C2×#131
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1626);