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C4×Q8×D191 #27133126

order12224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q8×D191

Splittings

FittingC4×Q8×C191 ⋊ C2
SylowC191 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D191
commutatorC2×C191C23×C4
FrattiniC22C23×D191
FittingC4×Q8×C191C2
socle, cosocleC22×C191C24
prime radicalC22×D191C23
hypercenterC4×Q8D191
hypocenterC191C2×C4×Q8
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofQ8⋊C8×D191, #37570913, #37570947, …
maximal normal subgroup ofQ8⋊C8×D191, #37570913, #37570947, …
maximal quotient ofC4×C4⋊C4×D191, C4×#20259287, C4×Q8×Dic191, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 1012);