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D4×Q8×C281 #31823144

order17984
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C281

Subgroups

subgroupG/H
center, socleC22×C281C24
commutator, Frattini, cosocleC22C24×C281
prime radicalC2×D4×C281C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

7025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49094406, #49094468, #49094552, …
maximal subgroup of#1627×C281, #1637×C281, #1649×C281, …
maximal normal subgroup of#1627×C281, #1637×C281, #1649×C281, …
maximal quotient ofQ8×C22⋊C4×C281, D4×C4⋊C4×C281, Q8×C4⋊C4×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 230);