Finite Group Databasebeta

C2×#13063270 #14583324

order2752
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13063270

Splittings

FittingC2×C16×C43 ⋊ C2
SylowC43 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22D344
commutator, cosocleC8×C43C23
FrattiniC8C22×D43
FittingC2×C16×C43C2
socleC22×C43D8
prime radicalC2×D344C2
hypercenterC2×C16D43
hypocenterC43C2×SD32
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 974);