Finite Group Databasebeta

C2×#20259834 #27135304

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

Aliases

direct productC2×#20259834

Splittings

SylowC193 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D193
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
FittingC2×M16×C193C2
socleC22×C193C4⋊C4
prime radicalC23×C193Q8
cosocleC2×C4×C193C23
hypercenterC2×M16D193
hypocenterC193C2×#108
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 594);