Finite Group Databasebeta

#564×C293 #34035825

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

Aliases

direct product#564×C293

Subgroups

subgroupG/H
center, socle, prime radicalC22×C293C24
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5567 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49158087, #49158113, #564×D293, …
maximal subgroup of#1658×C293, #1663×C293, C2×#564×C293, …
maximal normal subgroup of#1658×C293, #1663×C293, C2×#564×C293, …
maximal quotient of#2382×C293, #2719×C293, #2726×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 245);