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H(5,𝔽2)×C449 #28385243

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

Aliases

direct productH(5,𝔽2)×C449

Subgroups

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

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3592

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#43272175, #43272185, #43272194, …
maximal subgroup of#453×C449, #455×C449, B(4,𝔽2)×C449, …
maximal normal subgroup of#453×C449, #455×C449, B(4,𝔽2)×C449, …
maximal quotient of#518×C449, #520×C449, #534×C449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14368, 49);