Finite Group Databasebeta

C2×#27132679 #37581061

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

Aliases

direct productC2×#27132679

Splittings

FittingC22×M16×C191 ⋊ C2
SylowC191 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC22×M16×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC22×#15690287C2
cosocleC2×C4×C191C24
hypercenterC22×M16D191
hypocenterC191C2×#421
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

Conjugacy classes & character table

3844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13051);