Finite Group Databasebeta

C2×#13063265 #14583314

order2752
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13063265

Splittings

SylowC43 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D43
commutatorC2×C43C22×C8
FrattiniC8C22×D43
FittingC22×C8×C43C2
socleC22×C43C2×C8
prime radicalC23×C43C8
cosocleC8×C43C23
hypercenterC22×C8D43
hypocenterC43C2×M32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 964);