Finite Group Databasebeta

Q8×#14581712 #35420989

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#14581712

Splittings

FittingQ8×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ Q8×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingQ8×C4⋊C4×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenterQ8×C4⋊C4D83
hypocenterC83Q8×#102
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

1314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 186153);