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Q16×Dic179 #26038534

order11456
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ16×Dic179

Splittings

SylowC179 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC22D4×D179
commutatorC4×C179C22×C4
FrattiniC2×C4C22×D179
FittingC2×Q16×C179C2
socle, prime radicalC22×C179C2×D4
cosocleC2×C4×C179C23
hypercenterC2×Q16D179
hypocenterC179C4×Q16
LCSG ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#37510849, SD32×Dic179, #37510856, …
maximal normal subgroup of#37510849, SD32×Dic179, #37510856, …
maximal quotient ofQ16×C179⋊C8, #37507851, #37507897, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 644);