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C32×C5×AGL(1,𝔽5)×C23 #35208148

order20700
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×AGL(1,𝔽5)×C23

Splittings

Fitting, socle, HallC32×C52×C23 ⋊ C4
derivedC5 ⋊ C32×C4×C5×C23
HallC52×C23 ⋊ C32×C4
HallC32×C52 ⋊ C4×C23
SylowC52 ⋊ C32×C4×C23

Subgroups

subgroupG/H
center, hypercenterC32×C5×C23AGL(1,𝔽5)
commutator, hypocenterC5C32×C4×C5×C23
FrattiniC1G
Fitting, socleC32×C52×C23C4
prime radicalC32×C5×D5×C23C2
cosocleD5C2×C32×C5×C23
LCSG ▷ C5
UCSC1 ◁ C32×C5×C23

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4140

Conjugacy classes & character table

5175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 264);