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2−1+4×C449 #28385244

order14368
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C449 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C449

Subgroups

subgroupG/H
center, socleC2×C449C24
commutator, Frattini, cosocleC2C24×C449
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C449 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7184

Conjugacy classes & character table

7633 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#43272180, #43272190, #43272815, …
maximal subgroup of#454×C449, #456×C449, #577×C449, …
maximal normal subgroup of#454×C449, #456×C449, #577×C449, …
maximal quotient of#519×C449, #520×C449, #536×C449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14368, 50);