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Q82×C241 #29507407

order15424
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C241 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C241

Subgroups

subgroupG/H
center, socle, prime radicalC22×C241C24
commutator, Frattini, cosocleC22C24×C241
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C241 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

6025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44506523, #44506585, #44506666, …
maximal subgroup of#1623×C241, #1633×C241, #1645×C241, …
maximal normal subgroup of#1623×C241, #1633×C241, #1645×C241, …
maximal quotient ofQ8×C4⋊C4×C241, #2369×C241, #2451×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 239);