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C2×H(3,𝔽4)×C137 #31778537

order17536
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C25×C137 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×H(3,𝔽4)×C137

Subgroups

subgroupG/H
center, socleC23×C137C24
commutator, Frattini, cosocleC22C25×C137
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ G

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4384

Conjugacy classes & character table

5206 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC137×#8506, C137×#12763, C137×#12774, …
maximal normal subgroup ofC137×#8506, C137×#12763, C137×#12774, …
maximal quotient ofC2×#2375×C137, C2×#2379×C137, C4×H(3,𝔽4)×C137, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 2258);