Finite Group Databasebeta

C23×C4⋊(C83⋊C8) #36268012

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

Aliases

direct productC23×C4⋊(C83⋊C8)

Splittings

SylowC83 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D83
commutatorC2×C83C24×C8
FrattiniC2×C4C24×D83
FittingC23×C42×C83C2
socle, prime radicalC25×C83C2×C4
cosocleC2×C4×C83C25
hypercenterC23×C42D83
hypocenterC83C23×C4⋊C8
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C24×C4 ◁ C23×C42

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

5408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1033176);