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C7⋊#1042 #10622006

order700
isoclinismisoclinic class of C7⋊#1042
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊#1042

Splittings

Fitting, socle, derived, HallC52×C7 ⋊ C4
SylowC52 ⋊ Dic7
SylowC7 ⋊ #1042

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C7C4
prime radical, cosocleC5×C7×D5C2
LCSG ▷ C52×C7
UCSC1

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Polycyclic presentation:

2^2,5^2,7|a^2=b,c^a=c^2,d^a=d^4,e^a=e^6,c^b=c^4

Conjugacy classes & character table

73 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×#1042, D5×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×D35, …
maximal normal subgroup ofD7×#1042, D5×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×D35, …
maximal quotient ofC7⋊#6032, C2×C7⋊#1042, C3×C7⋊#1042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(700, 25);