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C3×AGL(1,𝔽5)×C179 #24924398

order10740
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C179 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C179

Splittings

Fitting, socle, HallC3×C5×C179 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C179
HallC5×C179 ⋊ C3×C4
HallC3×C5 ⋊ C4×C179

Subgroups

subgroupG/H
center, hypercenterC3×C179AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C179
FrattiniC1G
Fitting, socleC3×C5×C179C4
prime radicalC3×D5×C179C2
cosocleD5C2×C3×C179
LCSG ▷ C5
UCSC1 ◁ C3×C179

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2685 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×AGL(1,𝔽5)×C179, C32×AGL(1,𝔽5)×C179, C3×ΓL(1,𝔽16)×C179
maximal normal subgroup ofC9×AGL(1,𝔽5)×C179, C32×AGL(1,𝔽5)×C179
maximal quotient ofC9×AGL(1,𝔽5)×C179, C32×AGL(1,𝔽5)×C179, C3×ΓL(1,𝔽16)×C179

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10740, 10);