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C2×#63271 #10587727

order546
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC2×#63271

Splittings

Fitting, socle, HallC2×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C2×C3
HallC2×C13 ⋊ ΓL(1,𝔽8)
HallC2×C7 ⋊ C13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2#63271
commutator, cosocle, hypocenterC7×C13C2×C3
FrattiniC1G
Fitting, socleC2×C7×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C2

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 182

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(4,5,7)(6,9,12)(8,11,10)(13,15,14)(17,18,19)(20,22,21);(3,4,6,5,8,12,9,13,15,7,10,14,11)(16,17,19,21,18,20,22)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11763958, #11763962, #11763964, …
maximal normal subgroup of#11763958, #11763962, #11763964, …
maximal quotient ofC4×#63271, C22×#63271, C2×#11717942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(546, 16);