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#11765919⋊C4 #17987015

order4572
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#11765919⋊C4

Splittings

derived, SylowC127 ⋊ C4×C9
Hall#11765919 ⋊ C4
HallDic127 ⋊ C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC2#11765919⋊C2
commutator, hypocenterC127C4×C9
Fitting, socleC2×C127C2×C9
prime radical, cosocleC2×C127⋊C3C2×C3
LCSG ▷ C127
UCSC1 ◁ C2

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 131
transitive degreeμt(G) = 508

Polycyclic presentation:

2,3^2,127,2|a^2=e,b^3=c,d^a=d^126,d^b=d^68,d^c=d^107

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#11765919⋊C4, #11765919⋊Dic5, #11765919⋊AGL(1,𝔽5), …
maximal normal subgroup ofC5×#11765919⋊C4, (#11765919⋊C4)⋊C7, C7×#11765919⋊C4
maximal quotient ofC5×#11765919⋊C4, #11765919⋊Dic5, #11765919⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4572, 17);