Finite Group Databasebeta

C2×#27132637 #37580977

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#27132637

Splittings

SylowC191 ⋊ C2×#410

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
Fitting, prime radicalC22×#41×C191C2
socleC22×C191C2×C22⋊C4
cosocleC23×C191C24
hypercenterC22×#41D191
hypocenterC191C2×#410
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

788 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, 12967);