Finite Group Databasebeta

C2×#13063290 #14583363

order2752
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13063290

Splittings

SylowC43 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D43
commutatorC2×C43C23×C4
FrattiniC22C23×D43
FittingC2×C4⋊C4×C43C2
socle, prime radicalC23×C43C23
cosocleC22×C43C24
hypercenterC2×C4⋊C4D43
hypocenterC43C2×C4×Q8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1013);