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C2×H(3,𝔽4)×C107 #28334209

order13696
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C25×C107 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×H(3,𝔽4)×C107

Subgroups

subgroupG/H
center, socleC23×C107C24
commutator, Frattini, cosocleC22C25×C107
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

4066 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC107×#8506, C107×#12763, C107×#12774, …
maximal normal subgroup ofC107×#8506, C107×#12763, C107×#12774, …
maximal quotient ofC2×C107×#2375, C2×C107×#2379, C4×H(3,𝔽4)×C107, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 2258);