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Dic7×C52⋊C3 #14523569

order2100
isoclinismisoclinic class of D7×C52⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productDic7×C52⋊C3

Splittings

derived, HallC52×C7 ⋊ C3×C4
HallC52×Dic7 ⋊ C3
HallC7×C52⋊C3 ⋊ C4
SylowC52 ⋊ C3×Dic7
SylowC7 ⋊ C4×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D7×C52⋊C3
commutator, hypocenterC52×C7C3×C4
Fitting, socle, cosocleC2×C52×C7C2×C3
prime radicalC2×C7×C52⋊C3C2
LCSG ▷ C52×C7
UCSC1 ◁ C2

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52⋊C3×Dic49, C7×Dic7×C52⋊C3, #28413185, …
maximal normal subgroup ofC7×Dic7×C52⋊C3, C11×Dic7×C52⋊C3, C13×Dic7×C52⋊C3, …
maximal quotient ofC52⋊C3×Dic49, C7×Dic7×C52⋊C3, #28413185, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 49);