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C2×#773780 #72260337

order1024
nilpotency class2
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215×C4

Aliases

direct productC2×#773780

Subgroups

subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC24C26
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

101181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

(1,2);(11,12,13,14)(15,16,17,18);(7,8,9,10)(11,12,13,14)(15,16)(17,18);(8,10)(12,14)(15,16)(17,18);(4,6);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72233877, C2×#72233922, C2×#72219693, …
maximal normal subgroup ofC2×#72233877, C2×#72233922, C2×#72219693, …
maximal quotient ofC2×#72233926, C22×#773780, C2×#72293932, …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2), (11,12,13,14)(15,16,17,18), (7,8,9,10)(11,12,13,14)(15,16)(17,18), (8,10)(12,14)(15,16)(17,18), (4,6), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18));