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2−1+4×C461 #28414022

order14752
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C461 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C461

Subgroups

subgroupG/H
center, socleC2×C461C24
commutator, Frattini, cosocleC2C24×C461
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C461 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

7837 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44442249, #44442259, #44442884, …
maximal subgroup of#454×C461, #456×C461, #577×C461, …
maximal normal subgroup of#454×C461, #456×C461, #577×C461, …
maximal quotient of#519×C461, #520×C461, #536×C461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14752, 50);