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C2×H(3,𝔽4)×C139 #31804152

order17792
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C25×C139 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×H(3,𝔽4)×C139

Subgroups

subgroupG/H
center, socleC23×C139C24
commutator, Frattini, cosocleC22C25×C139
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4448

Conjugacy classes & character table

5282 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC139×#8506, C139×#12763, C139×#12774, …
maximal normal subgroup ofC139×#8506, C139×#12763, C139×#12774, …
maximal quotient ofC2×#2375×C139, C2×#2379×C139, C4×H(3,𝔽4)×C139, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 2258);