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D4×#3862 #11924263

order1176
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7

Aliases

direct productD4×#3862
unambiguous semidirect productC4⋊(C2×#3862)

Splittings

Fitting, HallC72×D4 ⋊ C3
SylowC72 ⋊ C3×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×#3862
commutator, socle, cosocleC2×C72C22×C3
FittingC72×D4C3
hypercenterD4#3862
hypocenterC72C3×D4
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ D4

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 84

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×ΓL(1,𝔽8)2, D4×#64425, S4×#3862, …
maximal normal subgroup ofD4×ΓL(1,𝔽8)2, D4×#64425, C2×D4×#3862, …
maximal quotient ofC2×D4×#3862, SD16×#3862, D8×#3862, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 178);