Finite Group Databasebeta

C8×#14581777 #35411367

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#14581777

Splittings

FittingC8×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ C8×#123

Subgroups

subgroupG/H
centerC22×C8C22×D83
commutatorC22×C83C23×C8
FrattiniC22×C4C23×D83
FittingC8×C4⋊C4×C83C2
socleC23×C83C23×C4
prime radicalC22×D332C2×C4
cosocleC22×C4×C83C24
hypercenterC8×C4⋊C4D83
hypocenterC83C8×#123
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 176531);