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C32×D5×C23 #14523396

order2070
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C23 · Schur multiplier (H2) = C3

Aliases

direct productC32×D5×C23
unambiguous semidirect productC5⋊(C2×C32×C23)

Splittings

Fitting, socle, HallC32×C5×C23 ⋊ C2
derived, SylowC5 ⋊ C2×C32×C23
HallC5×C23 ⋊ C2×C32
HallC32×C5 ⋊ C2×C23

Subgroups

subgroupG/H
center, hypercenterC32×C23D5
commutator, cosocle, hypocenterC5C2×C32×C23
FrattiniC1G
Fitting, socleC32×C5×C23C2
LCSG ▷ C5
UCSC1 ◁ C32×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1035

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(4,5,6)(8,11)(9,10)

Conjugacy classes & character table

828 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×AGL(1,𝔽5)×C23, C32×C23⋊AGL(1,𝔽5), C32×D5×D23, …
maximal normal subgroup ofC32×AGL(1,𝔽5)×C23, C32×C23⋊AGL(1,𝔽5), C32×D5×D23, …
maximal quotient ofC32×Dic5×C23, C2×C32×D5×C23, C3×C23×C5⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2070, 11);