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(C19⋊C3)⋊Dic7 #13097580

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

Aliases

unambiguous semidirect product(C19⋊C3)⋊Dic7

Splittings

derived, HallC7×C19 ⋊ C3×C4
HallDic133 ⋊ C3
HallC7×C19⋊C3 ⋊ C4
HallC19⋊C3 ⋊ Dic7
SylowC19 ⋊ C3×Dic7
SylowC7 ⋊ (C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC2(C19⋊C3)⋊D7
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

Polycyclic presentation:

2,3,2,7,19|a^2=c,d^a=d^6,e^a=e^18,e^b=e^11

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#18012151, #18012152, ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), …
maximal normal subgroup of#18012151, #18012152, ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), …
maximal quotient of#4294⋊Dic7, C3×(C19⋊C3)⋊Dic7, C3⋊((C19⋊C3)⋊Dic7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 3);