Finite Group Databasebeta

C2×#24916190 #36268295

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#24916190

Splittings

SylowC83 ⋊ C2×#2933

Subgroups

subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC2×C4C24×D83
Fitting, prime radicalC2×#525×C83C2
socleC23×C83C23×C4
cosocleC2×C4×C83C25
hypercenterC2×#525D83
hypocenterC83C2×#2933
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#525

2926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1033459);