Finite Group Databasebeta

C2×#24921971 #36311858

order21248
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#24921971

Splittings

FittingC2×#541×C83 ⋊ C2
SylowC83 ⋊ C2×#3557

Subgroups

subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#541×C83C2
socleC23×C83C25
prime radicalC2×#19128306C2
hypercenterC2×#541D83
hypocenterC83C2×#3557
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#541

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1077022);