Finite Group Databasebeta

C2×#24909183 #35557296

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24909183

Splittings

SylowC83 ⋊ C2×#2141

Subgroups

subgroupG/H
centerC23C2×#13050575
commutatorC8×C83C23×C4
FrattiniC2×C8C23×D83
FittingC23×Q16×C83C2
socleC23×C83C2×D8
prime radicalC24×C83D8
cosocleC2×C8×C83C24
hypercenterC23×Q16D83
hypocenterC83C2×#2141
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C23×Q16

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322460);