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Q16×Dic191 #27132758

order12224
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ16×Dic191

Splittings

SylowC191 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC22D4×D191
commutatorC4×C191C22×C4
FrattiniC2×C4C22×D191
FittingC2×Q16×C191C2
socle, prime radicalC22×C191C2×D4
cosocleC2×C4×C191C23
hypercenterC2×Q16D191
hypocenterC191C4×Q16
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#37574369, SD32×Dic191, #37574376, …
maximal normal subgroup of#37574369, SD32×Dic191, #37574376, …
maximal quotient ofQ16×C191⋊C8, #37571371, #37571417, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 644);