Finite Group Databasebeta

C2×#28410517 #44417241

order29248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28410517

Splittings

SylowC457 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D457
commutatorC2×C457C23×C4
FrattiniC22C23×D457
FittingC2×C4⋊C4×C457C2
socle, prime radicalC23×C457C23
cosocleC22×C457C24
hypercenterC2×C4⋊C4D457
hypocenterC457C2×C4×Q8
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C23 ◁ C2×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29248

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 1013);