Finite Group Databasebeta

C2×#24912442 #35575746

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#24912442

Splittings

SylowC83 ⋊ C2×#2545

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#124×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC22×#124D83
hypocenterC83C2×#2545
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#124

3310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 340910);