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C4⋊C4×C13⋊C3 #10597616

order624
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4⋊C4×C13⋊C3
unambiguous semidirect productC4⋊(C4×C13⋊C3)
unambiguous semidirect product(C13×C4⋊C4)⋊C3

Splittings

Fitting, HallC13×C4⋊C4 ⋊ C3
SylowC13 ⋊ C3×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×C13⋊C3
commutatorC2×C13C2×C3×C4
FittingC13×C4⋊C4C3
socle, cosocleC22×C13C22×C3
prime radicalC22×C13⋊C3C22
hypercenterC4⋊C4C13⋊C3
hypocenterC13C3×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4⋊C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#88047⋊C3, #88048⋊C3, #88049⋊C3, …
maximal normal subgroup of#88047⋊C3, #88048⋊C3, #88049⋊C3, …
maximal quotient of#95×C13⋊C3, C4⋊C8×C13⋊C3, #106×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(624, 53);