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2−1+4×C491 #30628241

order15712
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C491 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C491

Subgroups

subgroupG/H
center, socleC2×C491C24
commutator, Frattini, cosocleC2C24×C491
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C491 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7856

Conjugacy classes & character table

8347 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44536898, #44536908, #44537533, …
maximal subgroup of#454×C491, #456×C491, #577×C491, …
maximal normal subgroup of#454×C491, #456×C491, #577×C491, …
maximal quotient of#519×C491, #520×C491, #536×C491, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15712, 50);