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Q82×C281 #31823153

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

Aliases

direct productQ82×C281

Subgroups

subgroupG/H
center, socle, prime radicalC22×C281C24
commutator, Frattini, cosocleC22C24×C281
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49094381, #49094443, #49094524, …
maximal subgroup of#1623×C281, #1633×C281, #1645×C281, …
maximal normal subgroup of#1623×C281, #1633×C281, #1645×C281, …
maximal quotient ofQ8×C4⋊C4×C281, #2369×C281, #2451×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 239);