Finite Group Databasebeta

C2×#24905573 #35319328

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24905573

Splittings

SylowC83 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#14581712
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC22×#108×C83C2
socleC23×C83#102
prime radicalC24×C83SD16
cosocleC22×C8×C83C23
hypercenterC22×#108D83
hypocenterC83C2×#1387
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

614 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, 84492);