Finite Group Databasebeta

C4⋊Q8×D373 #37559963

order23872
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊Q8×D373

Splittings

FittingC4⋊Q8×C373 ⋊ C2
SylowC373 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC4⋊Q8×C373C2
prime radicalC22×D373C23
hypercenterC4⋊Q8D373
hypocenterC373C2×C4⋊Q8
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C4⋊Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

2632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1090);