Finite Group Databasebeta

Q8×C199⋊C16 #38770754

order25472
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productQ8×C199⋊C16

Splittings

SylowC199 ⋊ Q8×C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D199
commutatorC2×C199C22×C16
FittingC8×Q8×C199C2
socle, prime radicalC22×C199C22×C8
cosocleC2×C8×C199C23
hypercenterC8×Q8D199
hypocenterC199Q8×C16
LCSG ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C8 ◁ C8×Q8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25472

Conjugacy classes & character table

4040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 6414);