Finite Group Databasebeta

C2×#27132664 #37581032

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

Aliases

direct productC2×#27132664

Splittings

SylowC191 ⋊ C2×#417

Subgroups

subgroupG/H
centerC23C2×C22⋊D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting, prime radicalC22×#41×C191C2
socleC23×C191C2×D4
cosocleC2×C4×C191C24
hypercenterC22×#41D191
hypocenterC191C2×#417
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

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, 13022);