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C5×AGL(1,𝔽5)×C109 #24926263

order10900
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C109 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽5)×C109

Splittings

Fitting, socle, HallC52×C109 ⋊ C4
derivedC5 ⋊ C4×C5×C109
SylowC52 ⋊ C4×C109

Subgroups

subgroupG/H
center, hypercenterC5×C109AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C109
FrattiniC1G
Fitting, socleC52×C109C4
prime radicalC5×D5×C109C2
cosocleD5C2×C5×C109
LCSG ▷ C5
UCSC1 ◁ C5×C109

26 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2725 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×C109⋊C3, C3×C5×AGL(1,𝔽5)×C109, C5×ΓL(1,𝔽16)×C109
maximal normal subgroup ofC5×AGL(1,𝔽5)×C109⋊C3, C3×C5×AGL(1,𝔽5)×C109
maximal quotient ofC3×C5×AGL(1,𝔽5)×C109, C5×ΓL(1,𝔽16)×C109

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10900, 24);