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C7×#64470 #14523562

order2100
isoclinismisoclinic class of #3874
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#64470

Splittings

derived, HallC52⋊C3 ⋊ C4×C7
HallC7×C52⋊C3 ⋊ C4
HallC52×C7 ⋊ Dic3
SylowC52 ⋊ C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7#3874
commutator, hypocenterC52⋊C3C4×C7
FrattiniC2C7×#3874
Fitting, socleC2×C52×C7D3
prime radicalC2×C7×C52⋊C3C2
cosocleC2×C52⋊C3C2×C7
LCSG ▷ C52⋊C3
UCSC1 ◁ C2×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 420

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(8,14)(9,11,13,20,12,16,19,17,18,21)(10,22)(23,24,25,26);(8,9,11)(10,13,21)(12,17,15)(14,18,20)(16,22,19)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC49×#64470, C72×#64470, C7×C7⋊#64470, …
maximal normal subgroup ofC49×#64470, C72×#64470, C7×C11×#64470, …
maximal quotient ofC49×#64470, C72×#64470, C7×C7⋊#64470, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 42);