Finite Group Databasebeta

C2×#27132501 #37574821

order24448
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27132501

Splittings

SylowC191 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#20259263
commutator, cosocleC16×C191C23
FrattiniC16C22×D191
Fitting, prime radicalC2×D16×C191C2
socleC22×C191D16
hypercenterC2×D16D191
hypocenterC191C2×SD64
LCSG ▷ C16×C191 ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6811);