Finite Group Databasebeta

C2×#120×C293 #34035782

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C27

Aliases

direct productC2×#120×C293

Subgroups

subgroupG/H
center, socleC23×C293C23
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C293 ◁ G

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

8204 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49159194, #49159239, #49159908, …
maximal subgroup of#1889×C293, #1898×C293, #2021×C293, …
maximal normal subgroup of#1889×C293, #1898×C293, #2021×C293, …
maximal quotient ofC2×#379×C293, C2×#385×C293, C2×#386×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 202);