Finite Group Databasebeta

C2×#24906717 #35380235

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24906717

Splittings

SylowC83 ⋊ C2×#1650

Subgroups

subgroupG/H
centerC23#14581760
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#461×C83C2
socleC23×C83#120
prime radicalC22×D4×C83D4
hypercenterC2×#461D83
hypocenterC83C2×#1650
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 145399);