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Dic7×C19⋊C3 #13097579

order1596
isoclinismisoclinic class of D7×C19⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productDic7×C19⋊C3

Splittings

derived, HallC7×C19 ⋊ C3×C4
HallC19×Dic7 ⋊ C3
HallC7×C19⋊C3 ⋊ C4
SylowC19 ⋊ C3×Dic7
SylowC7 ⋊ C4×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D7×C19⋊C3
commutator, hypocenterC7×C19C3×C4
Fitting, socle, cosocleC2×C7×C19C2×C3
prime radicalC2×C7×C19⋊C3C2
LCSG ▷ C7×C19
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 532

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2)(3,4)(5,6,7,8,9,10,11)(13,14,16)(15,18,19)(17,21,20)(22,26,24)(23,27,25)(28,30,29);(1,3,2,4)(6,11)(7,10)(8,9)(12,13,15,19,24,29,26,14,17,22,27,16,20,25,18,23,28,30,21)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#18012153, #18012154, C19⋊C3×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup of#18012153, #18012154, C19⋊C3×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofDic7×#4294, C3×Dic7×C19⋊C3, C19⋊C3×Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 2);