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AGL(1,𝔽5)×C367 #20301150

order7340
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C367 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C367

Splittings

Fitting, socle, HallC5×C367 ⋊ C4
derived, SylowC5 ⋊ C4×C367

Subgroups

subgroupG/H
center, hypercenterC367AGL(1,𝔽5)
commutator, hypocenterC5C4×C367
FrattiniC1G
Fitting, socleC5×C367C4
LCSG ▷ C5
UCSC1 ◁ C367

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1835 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C367⋊C3, C3×AGL(1,𝔽5)×C367, ΓL(1,𝔽16)×C367, …
maximal normal subgroup ofAGL(1,𝔽5)×C367⋊C3, C3×AGL(1,𝔽5)×C367, C5×AGL(1,𝔽5)×C367
maximal quotient ofC3×AGL(1,𝔽5)×C367, ΓL(1,𝔽16)×C367, #1035×C367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7340, 6);