Finite Group Databasebeta

C2×#13063323 #14583441

order2752
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13063323

Splittings

SylowC43 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC23C22×D43
commutator, cosocleC22×C43C24
FrattiniC22C23×D43
FittingC22×Q8×C43C2
socle, prime radicalC23×C43C23
hypercenterC22×Q8D43
hypocenterC43C2×C4⋊Q8
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1091);