Finite Group Databasebeta

C22×C4⋊C8×D83 #36268010

order21248
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4⋊C8×D83

Splittings

FittingC22×C4⋊C8×C83 ⋊ C2
SylowC83 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D83
commutatorC2×C83C24×C8
FrattiniC2×C4C24×D83
FittingC22×C4⋊C8×C83C2
socleC24×C83C22×C4
prime radicalC24×D83C2×C4
cosocleC2×C4×C83C25
hypercenterC22×C4⋊C8D83
hypocenterC83C23×C4⋊C8
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1033174);