Finite Group Databasebeta

C2×#27132627 #37580956

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#27132627

Splittings

SylowC191 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC2×C4C23×D191
FittingC24×C4×C191C2
socleC23×C191C22×C4
prime radicalC25×C191C4
cosocleC2×C4×C191C24
hypercenterC24×C4D191
hypocenterC191C2×#407
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

Conjugacy classes & character table

6136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 12946);