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D276 #10587787

order552
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD276
unambiguous semidirect productC4⋊D69

Splittings

FittingC3×C4×C23 ⋊ C2
HallC3×C23 ⋊ D4
SylowC23 ⋊ D12
SylowC3 ⋊ D92

Subgroups

subgroupG/H
center, FrattiniC2C2×D69
commutator, socle, cosocleC2×C3×C23C22
FittingC3×C4×C23C2
hypercenterC4D69
hypocenterC3×C23D4
LCSG ▷ C2×C3×C23 ▷ C3×C23
UCSC1 ◁ C2 ◁ C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 276

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

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

Polycyclic presentation:

2^3,3,23|b^2=c,b^a=bc,d^a=d^2,e^a=e^22

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764137, #11764138, #11764142, …
maximal normal subgroup of#11764137, #11764138, #11764142, …
maximal quotient of#11764190, D552, Dic276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 25);