Finite Group Databasebeta

← Prev (#14579796) Next (#14579798) →

C41×#329 #14579797

order2624
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C2×C4×C41 · Schur multiplier (H2) = C2

Aliases

direct productC41×#329

Subgroups

subgroupG/H
center, socleC22×C41C22⋊C4
commutatorC2×C4C2×C4×C41
Frattini, cosocleC42C22×C41
prime radicalC2×D4×C41C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1312

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(42,43,44,47,45,46,48,49)(51,54,55,56);(43,46)(44,48)(50,51)(52,56)(53,55)(54,57)

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×#1403, C41×#1404, C2×C41×#329, …
maximal normal subgroup ofC41×#1403, C41×#1404, C2×C41×#329, …
maximal quotient ofC41×#1270, C41×#1272, C41×#1295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 10);